A singularly perturbed linear two-point boundary-value problem

We consider the following singularly perturbed linear two-point boundary-value problem:

Ly(x) ≡ Ω(ε)D_xy(x) - A(x,ε)y(x) = f(x,ε) 0≤x≤1 (1a)

By ≡ L(ε)y(0) + R(ε)y(1) = g(ε) ε → 0^+ (1b)

Here Ω(ε) is a diagonal matrix whose first m diagonal elements are 1 and last m elements are ε. Aside from reasonable continuity conditions placed on A, L, R, f, g, we assume the lower right mxm principle submatrix of A has no eigenvalues whose real part is zero. Under these assumptions a constructive technique is used to derive sufficient conditions for the existence of a unique solution of (1). These sufficient conditions are used to define when (1) is a regular problem. It is then shown that as ε → 0^+ the solution of a regular problem exists and converges on every closed subinterval of (0,1) to a solution of the reduced problem. The reduced problem consists of the differential equation obtained by formally setting ε equal to zero in (1a) and initial conditions obtained from the boundary conditions (1b). Several examples of regular problems are also considered.

A similar technique is used to derive the properties of the solution of a particular difference scheme used to approximate (1). Under restrictions on the boundary conditions (1b) it is shown that for the stepsize much larger than ε the solution of the difference scheme, when applied to a regular problem, accurately represents the solution of the reduced problem.

Furthermore, the existence of a similarity transformation which block diagonalizes a matrix is presented as well as exponential bounds on certain fundamental solution matrices associated with the problem (1).

To pave or not to pave: A social landscape analysis of land use decision-making in the towns of the lamprey watershed

Population pressure in coastal New Hampshire challenges land use decision-making and threatens the ecological health and functioning of Great Bay, an estuary designated as both a NOAA National Estuarine Research Reserve and an EPA National Estuary Program site. Regional population in the seacoast has quadrupled in four decades resulting in sprawl, increased impervious surface cover and larger lot rural development (Zankel, et.al., 2006). All of Great Bay’s contributing watersheds face these challenges, resulting in calls for strategies addressing growth, development and land use planning. The communities within the Lamprey River watershed comprise this case study. Do these towns communicate upstream and downstream when making land use decisions? Are cumulative effects considered while debating development? Do town land use groups consider the Bay or the coasts in their decision-making? This presentation, a follow-up from the TCS 2008 conference and a completed dissertation, will discuss a novel social science approach to analyze and understand the social landscape of land use decision-making in the towns of the Lamprey River watershed. The methods include semi-structured interviews with GIS based maps in a grounded theory analytical strategy. The discussion will include key findings, opportunities and challenges in moving towards a watershed approach for land use planning. This presentation reviews the results of the case study and developed methodology, which can be used in watersheds elsewhere to map out the potential for moving towns towards EBM and watershed-scaled, land use planning. (PDF contains 4 pages)

Utilization of some aquatic macrophytes in Nigeria in-land water bodies: a review

Aquatic vegetation is an essential component of the aquatic ecosystem with both positive and negative implications on the water body. Efforts are always made to curtail the excessive growth of aquatic plants in order to prevent them from becoming a nuisance in the ecosystem. One of the ways of solving such problem is the positive economic use of such plants. Utilization as a method of weed control within the aquatic ecosystem is considered to be one of the safest methods of weed control as this provides the riparian communities double advantages in terms of save environment and personal benefits of the plant. The flora diversity of freshwater and brackish environments posses a great potential to both man and higher animals alike. Due to this fact, this paper attempt to review the exploited and unexploited aquatic plants resources of many of our water bodies in Nigeria both economica/ly and socially, to the populace. Recommendations are also advanced for further studies that will enhance sound management of the resources for maximum benefits and sustainability

Breaking the 400 ppm barrier: Physical and Social implications of the recent CO2 rise

6 p.

Rompiendo la barrera de las 400 ppm: implicaciones físicas y sociales del reciente aumento de CO2

6 p.

400 ppm-ko langa hautsi da: CO2-kontzentrazioaren igoeraren ondorio fisiko eta sozialak

6 p.

Competing Ecosystem services: an Assessment of Carbon and timber in the Tropical forests of Central America

4 p.

Competing Ecosystem Services: an Assessment of Carbon and Timber in the Tropical Forests of Central America

29 p.

Value chain analysis for sea cucumber in the Philippines

This study examined the sea cucumber industry in the Philippines through the value chain lens. The intent was to identify effective pathways for the successful introduction of sandfish culture as livelihood support for coastal communities. Value chain analysis is a high-resolution analytical tool that enables industry examination at a detailed level. Previous industry assessments have provided a general picture of the sea cucumber industry in the country. The present study builds on the earlier work and supplies additional details for a better understanding of the industry's status and problems, especially their implications for the Australian Center for International Agricultural Research (ACIAR) funded sandfish project "Culture of sandfish (Holothuria scabra) in Asia- Pacific" (FIS/2003/059). (PDF contains 54 pages)

Value Estimation and Comparison in Multi-Attribute Choice

The following work explores the processes individuals utilize when making multi-attribute choices. With the exception of extremely simple or familiar choices, most decisions we face can be classified as multi-attribute choices. In order to evaluate and make choices in such an environment, we must be able to estimate and weight the particular attributes of an option. Hence, better understanding the mechanisms involved in this process is an important step for economists and psychologists. For example, when choosing between two meals that differ in taste and nutrition, what are the mechanisms that allow us to estimate and then weight attributes when constructing value? Furthermore, how can these mechanisms be influenced by variables such as attention or common physiological states, like hunger?

In order to investigate these and similar questions, we use a combination of choice and attentional data, where the attentional data was collected by recording eye movements as individuals made decisions. Chapter 1 designs and tests a neuroeconomic model of multi-attribute choice that makes predictions about choices, response time, and how these variables are correlated with attention. Chapter 2 applies the ideas in this model to intertemporal decision-making, and finds that attention causally affects discount rates. Chapter 3 explores how hunger, a common physiological state, alters the mechanisms we utilize as we make simple decisions about foods.

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

On the uniqueness of singular solutions to boundary-initial value problems in linear elastodynamics

This investigation deals with certain generalizations of the classical uniqueness theorem for the second boundary-initial value problem in the linearized dynamical theory of not necessarily homogeneous nor isotropic elastic solids. First, the regularity assumptions underlying the foregoing theorem are relaxed by admitting stress fields with suitably restricted finite jump discontinuities. Such singularities are familiar from known solutions to dynamical elasticity problems involving discontinuous surface tractions or non-matching boundary and initial conditions. The proof of the appropriate uniqueness theorem given here rests on a generalization of the usual energy identity to the class of singular elastodynamic fields under consideration.

Following this extension of the conventional uniqueness theorem, we turn to a further relaxation of the customary smoothness hypotheses and allow the displacement field to be differentiable merely in a generalized sense, thereby admitting stress fields with square-integrable unbounded local singularities, such as those encountered in the presence of focusing of elastic waves. A statement of the traction problem applicable in these pathological circumstances necessitates the introduction of "weak solutions'' to the field equations that are accompanied by correspondingly weakened boundary and initial conditions. A uniqueness theorem pertaining to this weak formulation is then proved through an adaptation of an argument used by O. Ladyzhenskaya in connection with the first boundary-initial value problem for a second-order hyperbolic equation in a single dependent variable. Moreover, the second uniqueness theorem thus obtained contains, as a special case, a slight modification of the previously established uniqueness theorem covering solutions that exhibit only finite stress-discontinuities.